Question

For the functions f(x) = –3x^2 – 10x and g(x) = 4x^2, find (f – g)(x) and (f - g)(1).

a) (f - g)(x) = -7x^2 - 10x; (f - g)(1) = -17
b) (f - g)(x) = x^2 + 10x; (f - g)(1) = 9
c) (f - g)(x) = -7x^2 + 10x; (f - g)(1) = -1
d) (f - g)(x) = -7x^2 - 14x; (f - g)(1) = -21

Answer 1

The correct answer to the student's mathematics question is option a, where (f - g)(x) equals -7x^2 - 10x, and (f - g)(1) evaluates to -17.

Step-by-step explanation:

The student has been tasked with finding the difference of the functions f(x) and g(x), denoted as (f - g)(x), and then evaluating this difference when x equals 1, or (f - g)(1).

The first step is to express the difference between the functions:

(f - g)(x) = f(x) - g(x) = (-3x^2 - 10x) - (4x^2).

Combining like terms:

(f - g)(x) = -3x^2 - 10x - 4x^2 = -7x^2 - 10x.

Next, to evaluate (f - g)(1), we substitute x = 1 into the equation we found:

(f - g)(1) = -7(1)^2 - 10(1) = -7 - 10 = -17.

So, the correct answer is:

(f - g)(x) = -7x^2 - 10x; (f - g)(1) = -17, which corresponds to option a.